Download 4 Maths Curriculum Plan 09-10

St. Francis’ Canossian College
Mathematics Department Curriculum Planning 09-10
Subject:
Mathematics
Subject Teacher: Ms. S. Wong (4A), Ms J. Ho (4B), Mr K.M.Tang (4C), Ms Q. Kwok (4D)
Textbook:
NSS Mathematics in Action (4A and 4B) -- Longman
Class: Form 4
First Term
Open Book Assessment
2- 3 times (Sept – Oct)
*CAS
Ms. J. Ho
First Term Common Quiz (1)
30 mins (in Nov)
*CAS
Ms. Q. Kwok
First Term Common Quiz (2)
~ 40 mins (in Dec)
20% exam report
Mr. K. M. Tang
First Term Exam
1 paper only (Jan)
60%
Ms. S. Wong
Chapter Quiz
Once per chapter
*CAS
Teacher may set their own quiz
SBA (1) -- Trial
Around March
/
Ms. Q. Kwok
Second Term Common Test
Around April
20% exam report
Ms. S. Wong
SBA (2)
Around May
5% exam report
Ms. Q. Kwok
Final Exam
June
60%
Paper I: Ms. J. Ho
Paper II: Mr. K. M. Tang
Second Term
*Other CAS elements may include: HW & corrections, Classroom Performance, ..etc
Common Lesson Arrangement: 4A & 4B -- Day 2 8th, 9th lesson; Day 4 8th, 9th lesson;
4C & 4D – Day 5 1st, 2nd lesson
Month
Ch.
Sept
1
Objectives
Quadratic Equations in One Unknown (I)
Detailed Contents
1.1 To learn the hierarchy of the real number system
 Integers, rational numbers, irrational numbers and real numbers
 Conversion between recurring decimals and fractions
1.2 To solve quadratic equations by factor method
2
 General form of a quadratic equation: ax  bx  c  0 where a  0.
 Factoring quadratic polynomials and hence solving quadratic equation
 Do NOT cancel common polynomial factor or with x on both sides of an
equation.
 Demonstrate that some quadratic equations can be solved using identities or
by taking square root on both sides.
1.3 To solve quadratic equations by quadratic formula
 Solving quadratic equations using the quadratic formula
 Simplifying expressions involving 2 ± 48 (NF)
1.4 To solve quadratic equations by the graphical
method
 Plotting the graph of y = ax2 + bx + c and noting the x-intercepts to determine
the roots of the quadratic equation ax2 + bx + c = 0.
1.5 Forming a quadratic equation with given roots
 The given roots are confined to real numbers.
1.6 Problems leading to solving Quadratic Equations
 Problems should be related to students’ experience, eg, applications in
dealing with numbers, measurement, travel and other daily life problems.
 Problems involving complicated equations like
foundation. (NF)
6
6
+
= 5 is nonx
x 1
Sept
2
Quadratic Equations in One Unknown (II)
1.
To understand the discriminant of a quadratic equation
2
 The discriminant [  b  4ac] of a quadratic equation
2.
To understand the relations between the discriminant of
a quadratic equation and the nature of its roots
 The number of roots of a quadratic equation as indicated by  >0,  =0 and  <0
3.
To understand the relations between the roots and
coefficients of a quadratic equation (NF)
4.
Oct
3
 The nature of roots as indicated by  <0 (complex roots) and   0 (real roots)
 += 
To form quadratic equations using these relations (NF)
b
c
and   =
a
a
Functions and Graphs
1. recognise the intuitive concepts of functions, domains and
co-domains, independent and dependent variables
 A function is a relationship between an independent variable x and a dependent
variable y in such a way that one value of x gives exactly one value of the dependent
variable y.
 To identify whether a given relation is a function or not from a given equation, a set
of tabulated values of x and y, or from its graph.

2. recognise the notation of functions and use tabular,
algebraic and graphical methods to represent functions
Finding the domain of a function is required but need not be stressed.
 The function notation: f(x), H(x), g(x) etc.
 The dummy nature of the independent variable
 Values of a function
 The constant function and its graph: y=c or f(x) = c
 Representations like
are also accepted
 The linear function and its graph: y=ax+b or f(x) = ax+b where a  0
and it is the slope of the straight line graph while b is the y-ntercept.[optional]
3. understand the features of the graphs of quadratic
functions
 The quadratic function and its graph: y=ax2+bx+c or f(x) = ax2+bx+c
 The properties of the graph deduced from the given graph
- the direction of opening as deduced from the value of a
- the axis of symmetry
- the vertex (also determine whether it is the maximum point or the minimum point)
- relations with the axes (eg the x- and y-intercepts)
4. find the maximum and minimum values of quadratic
functions by the algebraic method (NF)
Oct Nov
4

Students are expected to find the max and min by graphical method

Students are expected to solve problems relating to max and min

The definitions include
Exponential Functions
1. To understand the meaning of rational indices [NF]
1
expressions such as
3
n
m
a , a n and a n . Students are also expected to evaluate
8 .
2. To learn the laws of rational indices [NF]
3. To solve exponential equations [NF]
4. To learn the definition of exponential function and its
graph [NF]

Solving exponential equations involving integral indices

The following properties and features are included:
- the domains of the functions
- the function f (x) = a x increases (decreases) as x increases for a > 1 (0 < a < 1)
- the intercepts with the axes
- the rate of increasing/the rate of decreasing (by direct inspection)
Nov Dec
5
Logarithmic Functions
1.
understand the definition and properties of logarithms
(including the change of base) [NF]
2. understand the properties of logarithmic functions and
recognise the features of their graphs [NF]
3. solve logarithmic equations [NF]
4. appreciate the applications of logarithms in real-life
situations [NF]
 The definition of logarithms
 Properties of logarithms

-
The following properties and features are included:
the domains of the functions
y = a x is symmetric to y = log a x about y = x
the intercepts with the axes
the rate of increasing/the rate of decreasing (by direct inspection)
 Solving logarithmic equations
 Applications of Logarithms in Real-life Situations
- Sound intensity and sound intensity level
- The Richter Scale
Civic Education: environmental protection against noise pollution
Cross-curricula integration: the use of maths in the study of physics and geography
5. appreciate the development of the concepts of logarithms
[NF]
Jan 2010
Jan
 The topics such as the historical development of the concepts of logarithms
and its applications to the design of some past calculation tools such as slide
rules and the logarithmic table may be discussed.
First Term Examination
6
Equations of Straight lines
1. understand the equation of a straight line
 Students are expected to find the equation of a straight line from given conditions
such as:
- the coordinates of any two points on the straight line
- the slope of the straight line and the coordinates of a point on it
- the slope and the y-intercept of the straight line
 Students are expected to describe the features of a straight line from its equation.
The features include: the slope, the intercepts with the axes, whether it passes
through a given point
 The normal form is not required.
2. understand the possible intersection of two straight lines
Feb
7
 Students are expected to determine the number of intersection points of two straight
lines from their equations.
More about Polynomials (I)
1. perform division of polynomials
2. To learn the Remainder Theorem and apply it to find the
remainder in divisions of polynomials
3. To learn the Factor Theorem and apply it to factorize
polynomials
 Application of the Factor Theorem to factorize cubic polynomials
Feb
8
More about Polynomials (II)
1. understand the concepts of the greatest common divisor
and the least common multiple of polynomials [NF]
2.
perform addition, subtraction, multiplication and division
of rational functions [NF]
 The terms “H.C.F.” , “gcd”, etc. can be used.
 Computation of rational functions with more than two variables is not required
SBA (1)
Mar
9
Simultaneous equations: 1 linear & 1 quadratic
1. To solve simultaneous equations, one linear and one
quadratic, graphically [NF]
2. To solve simultaneous equations, one linear and one
quadratic, by algebraic method [NF]
 To find the equation of the straight line needed to be drawn on the given graph of the
quadratic function in order to solve a quadratic equation
 Understand the use and limitations of the graphical method in solving equations.
3. solve equations (including fractional equations,
 To determine the number of real solutions of the system of equations, one quadratic
and one linear by the algebraic method [substitution of the linear equation to the
quadratic equation and then determine by the value of the discriminant]
exponential equations, logarithmic equations and
trigonometric equations) which can be transformed into
quadratic equations [NF]
 Solutions for trigonometric equations are confined to the interval from 0° to
360° .
4. solve problems involving equations which can be
transformed into quadratic equations [NF]
Mar
12
Variations
1. To learn the different relationships between two changing
 Rate, ratio and proportion
quantities
2. To learn the algebraic and graphical representations of
two quantities in direct variation.
 Direct variation of two quantities and the graph of the variation of the two quantities.
 Examples may include those in real-life situations or from other subjects
3. To learn the algebraic and graphical representation of
 Inverse variation of two quantities and the graph of the variation of the two
quantities.
two quantities in inverse variations
4. To learn joint and partial variations
 Joint variation and partial variation
5. To apply different variations to solve real-life problems
Mar
Apr
SBA (2)
10
More About Trigonometry (I)
1. understand the functions sine, cosine and tangent
2. To learn the definition of trigonometric ratios of angles
less than 90o using a right-angled triangle
3. To learn some basic trigonometric identities
4. To learn the general definition of trigonometric ratios of
any angle
5. To learn the graphs of trigonometric functions
6. To learn the properties of trigonometric functions from
their graphs
7. Other Trigonometric Identities
8. To solve trigonometric equations
 Basic definition of trigonometric ratios in terms of the ratios of the sides of a rightangled triangle.
 Trigonometric ratios of special angles: 30o, 45o, 60o
 Five basic trigonometric identities:
- sin2x + cos2x = 1
- tanx = sinx/cosx
- sin (90o-x) = cos x
- cos(90o-x) = sin x
- tan (90o-x) = 1/tanx
 Angles of rotation
 The four quadrants and co-terminal angles
 Trigonometric ratios of any angle
 The signs of trigonometric ratios
 The graphs and properties of the sine, cosine and tangent functions, including
maximum and minimum values
 The periodicity of the trigonometric functions
 Trigonometric functions of the forms y=f(x) + k, y=kf(x) and y= f(kx)
 Trigonometric ratios of -  , (90 0   ) , (180 0   ) and (360 0   )
 solve the trigonometric equations a sin θ = b , a cos θ = b , a tan θ = b (solutions
in the interval from 0° to 360° ) and other trigonometric equations (solutions in
the interval from 0° to 360° ) [NF]
 Equations that can be transformed into quadratic equations are required only in
the Non-foundation Topics [NF]
IT Activity
 To explore the signs of trigonometric ratios of angles in different quadrants
 To plot and explore the graph of sine function
Apr
May
Second Term Common Test
11
Applications of Trigonometry in 2D problems
1. To learn the formula ½ absinC and the Heron’s formula
and apply them to find the areas of triangles [NF]
2. To learn the sine and cosine formula and apply them to
solve triangles [NF]
3. To learn the Heron’s formula [NF]







Area of triangle
The formula ½ ab sinC and the Heron’s formula
The Sine Formula
The Cosine Formula
Application of the sine and cosine formula to solve 2-dimensional problems.
The Heron’s Formula
Application of the Heron’s formula to solve 2-dimensional problems.
4. use the above formulae to solve 2-dimensional problems
[NF]
May
June
Revision
Final Exam